Abstract
We discuss the regularized boundary state \( {e}^{-{\tau}_0H}\Big|{\left.B\right\rangle}_a \) on two aspects in both 2D CFT and higher dimensional free field theory. One is its entanglement and correlation properties, which exhibit exponential decay in 2D CFT, the parameter 1/τ0 works as a mass scale. The other concerns with its time evolution, i.e., \( {e}^{-itH}{e}^{-{\tau}_0H}\Big|{\left.B\right\rangle}_a \). We investigate the Kubo-Martin-Schwinger (KMS) condition on correlation function of local operators to detect the thermal properties. Interestingly we find the correlation functions in the initial state \( {e}^{-{\tau}_0H}\Big|{\left.B\right\rangle}_a \) also partially satisfy the KMS condition. In the limit t → ∞, the correlators will exactly satisfy the KMS condition. We generally analyse quantum quench by a pure state and obtain some constraints on the possible form of 2-point correlation function in the initial state if assuming they satisfies KMS condition in the final state. As a byproduct we find in an large τ0 limit the thermal property of 2-point function in \( {e}^{-{\tau}_0H}\Big|{\left.B\right\rangle}_a \) also appears.
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Guo, Wz. Entanglement properties of boundary state and thermalization. J. High Energ. Phys. 2018, 44 (2018). https://doi.org/10.1007/JHEP06(2018)044
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DOI: https://doi.org/10.1007/JHEP06(2018)044